matemàtiques límits

lim[h-->0][ ( sin(h)/h ) ] = lim[h-->0][ (1/h)·( h+(-1)·(1/3!)·h^{3}+... ) ] = 1

lim[h-->0][ ( sinh(h)/h ) ] = lim[h-->0][ (1/h)·( h+(1/3!)·h^{3}+... ) ] = 1

lim[h-->0][ ( (cos(h)+(-1))/h^{2} ) ] = ...

... lim[h-->0][ (1/h^{2})·( 1+(-1)·(1/2!)·h^{2}+...+(-1) ) ] = (-1)·(1/2)

lim[h-->0][ ( (cosh(h)+(-1))/h^{2} ) ] = ...

... lim[h-->0][ (1/h^{2})·( 1+(1/2!)·h^{2}+...+(-1) ) ] = (1/2)

arc-cos(x)+arc-sin(x) = (pi/2)

arc-cos(1)+arc-sin(1) = 0+(pi/2)

arc-cos(-1)+arc-sin(-1) = pi+(3/2)·pi

arc-cos(0)+arc-sin(0) = (pi/2)+0

arc-cos(-0)+arc-sin(-0) = (3/2)·pi+pi

arc-cos(2^{(1/2)}/2)+arc-sin(2^{(1/2)}/2) = (1/4)·pi+(1/4)·pi

arc-cos((-1)·(2^{(1/2)}/2))+arc-sin((-1)·(2^{(1/2)}/2)) = ...

... (-1)·(3/4)·pi+(-1)·(3/4)·pi = (-1)·(pi/2)+(-1)·pi